3. According to the study, 20% of children with brain cancer undergo surgery and

Question

3. According to the study, 20% of children with brain cancer undergo surgery and the rest of them receive the traditional treatment (chemotherapy or radiation). If children have the surgery, they are cured 95% of the time. If children receive the traditional treatment (chemotherapy or radiation), they are cured 65% of the time. (a) What is the probability that a randomly selected child (with cancer) undergoes the surgery and is cured? (b) What is the probability that a randomly selected child (with cancer) undergoes the surgery, but is not cured? (c) What percent of children (with cancer) are cured? 4. The prisoner is given 20 chips (10 white chips and 10 black chips). He will place the chips into two identical boxes as he wishes. The only restriction is that each box must contain at least one chip. The executioner will then pick one of the two boxes at random, and then select one chip from the selected box. If the chip is white, the prisoner will then be set free. (a) Suppose that the prisoner places one white chip in one box and the rest in the other box. What is the probability that he will be free? (b) Suppose that the prisoner places 5 white and 5 black chips in one box and the rest in the other box. What is the probability that he will be free?

Explanation / Answer

Ans:

Given that

P(surgery)=0.2

P(traditional)=1-0.2=0.8

P(cured/surgery)=0.95

P(not cured/surgery)=1-0.95=0.05

P(cured/taditional)=0.65

a)P(surgery and cured)=P(cured/surgery)*P(surgery)=0.95*0.2=0.19

b)P(surgery and not cured)=P(not cured/surgery)*P(surgery)=0.05*0.2=0.01

c)P(cured)=P(cured/surgery)*P(surgery)+P(cured/traditional)*P(traditional)

=0.95*0.2+0.65*0.8=0.71

  

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